Why doesn't Connect Vertices create an edge as opposed to Make Edge/Face?
The difference between them is that Connect Vertices tool cuts through already exhisting geometry (just like Knife Tool), whereas Make Edge/Face creates new one.

In the proposed scenario it's hard to see the difference, so to better demonstrate it I used side of the cube.

Connect Vertices



The tool will cut through exhisting geometry based on selected vertices which belong to the same face (so if I selected 3 vertices where one vertice per face, there wouldn't be any effect)

Connect Vertex Path 

(I decided to put it also here because for some time I couldn't get the difference)


The result of using Connect Vertex Path command (J). The order of selecting vertices is important; whether vertices belong to the same face is not. The adjacent faces were splitted, becoming tris now.

Make Edge/Face



Make Edge/Face (F) will simply create new face there atop of exhisting one, not splitting anything.